Many, many times I've bought a set of new tires with balance, had them shake like a [censored], took them home, chucked them on the bubble balancer, and a static balance on one of them came out WAY better than the dynamic balance on the electronic machine. Go figure.
I've watched many shops balance my tires, have them zero balance it, then have them rotate the wheel 90* on the machine and spin them again...calls for weight 50% of the time.
Also, if it's WAY off, the correct fix (IMHO) is to try and spin the tire 180* and see if it gets better. I've gone so far as to spin the wheel, weight the wheel so it spins zero (static), put the tire back on and spin the assembly up, mark where it's calling for weight on the tire, and align that and the wheel weight 180* apart, remove the wheel weight, then balance from there. Aircraft wheels and tires are already marked for this, and for the life of me, I can't figure out why they don't do it with car wheels/tires.
Now I did work in a shop once where they had the electronic off the car machine and it's repeatability was awful or non-existent. So you never wanted to recheck as you would end up playing with it and chasing it for hours. But when you road tested the car it was smooth. But what I have actually found today is that the "new" tires are made so much better and if push comes to shove you may be able to get away without the precision balance. I truly believe that is how so many get by with the bubble balancers as you're just getting it a lot closer then it was.
The guy that balanced your tires might have been selling burgers at McDonalds last week. That's why I recommend going to that older shop, his equipment is paid for, and knows it like the back of his hands, I would prefer doing it myself, but outside of a bubble level I have no room. The nice expensive machines are only as good as the guy doing the work.